in Singly and Doubly Refracting Media. 421 



responds a determinate compatibility on the part of the asthe- 

 real and corporeal particles ; and the resistance called forth by 

 the presence of the latter now comes into play as a partial com- 

 ponent {a. 1 6 1 cos 8 ly ct 2 e 2 cos &>) in a direction (V , h' w c' ; 

 a" w b /f 0J c"q) depending on the effective molecular quality. 

 Here, therefore, afterwards as before, 8 denotes the angle be- 

 tween a definite compound series of molecules a, b, c, resulting 

 from the modification, and a simple constituent thereof in its 

 unmodified position. Hence we may, and must, attribute to 

 one and the same ray any number of partial normals and ex- 

 citing partial waves, all of which combine into a resultant 

 normal and wave ; and this resultant is obtained when we 

 erect on the corresponding radius of our direct ellipsoid a tan- 

 gential plane and let fall a perpendicular upon it. The plane 

 determined by the radius vector and the normal is then the 

 resultant vibration-plane ; and the angle A between them 

 becomes the resultant angle between the ray and the resultant 

 normal ; so that we get 



oj = a cos A (25) 



If now the various kinds of mass-particles are modified by 

 the partial pressures applied in identical axial directions, or 

 rather, when we introduce corresponding molecular forces, if 

 the structure constituted by the individual heterogeneous ele- 

 ments is arranged symmetrically about the same directions, 

 this corresponds to the case of the regular system of crystals ; 

 but does it consist of a grouping about divergent axial direc- 

 tions, then we have what is called the dispersion of the optical 

 axes, which has hitherto seemed to mock all attempts to ex- 

 plain it. 



11. Let us now, for anisotropic media also, turn from the 

 moving forces to the vires vivce. For this purpose let us con- 

 struct the plane of vibration corresponding to a determined 

 colour and direction of the ray, and in it a parallelogram 

 LMNO, making its longer side L parallel to the ray and 

 equal to V , giving to the shorter side ON the length 

 (A = A cos A) of the actual amplitude and making it coincide 

 with the direction of vibration of the aether particles, so that 

 consequently it will be perpendicular to the resultant normal 

 and the angle LONbe equal to 90° + A. 



Let us further imagine the sethereal and corporeal particles 

 situated within it brought out of their position of equilibrium 

 into an extreme position such as would correspond to a wave 

 characterized by A, V ', and somehow kept fixed therein. The 

 elasticity thereby accumulated is again the same as if the cor- 

 poreal particles were not present. If the medium be then left 

 to itself, the aether particles will press back in oblique paths of 



